A SECOND ORDER RELATIVE MOTION MODEL FOR GATEWAY

Current Gateway rendezvous, proximity operations, and docking plans are limited to segments of the Gateway orbit far from the moon due to highly nonlinear dynamics as Gateway approaches perilune, which stress existing relative motion models. This work introduces a preliminary version of the Quadratic Interpolated State Transition (QIST) relative motion model as a closed-form second order model that provides accurate relative trajectory prediction for the entire Gateway orbit including the difficult region surrounding perilune. The QIST model utilizes interpolated state transition tensors of a Gateway reference orbit, used to propagate arbitrary relative motion trajectories without numerical integration of the relative trajectory. Further, the underlying periodicity of the Gateway orbit used in the new model makes it valid for relative trajectories of arbitrary duration while only storing interpolant information for a single Gateway period. The memory footprint of the precomputed interpolants is considered relative to the interpolant accuracy, with the highest fidelity model requiring 250 kB, and reduced accuracy models needing 150 kB of memory to store the interpolant coefficients. The new model's interpolation and state transition tensor generation scheme is validated by comparing a propagation using interpolated tensors to one using integrated tensors. Both the first- and second-order interpolated state updates are shown to agree with the updates obtained by integration to double precision.